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JEE Main & Advanced Physics Transmission of Heat Question Bank Radiation Stefan's law

  • question_answer
    Two spheres \[P\] and \[Q\], of same colour having radii \[8\ cm\] and \[2\ cm\] are maintained at temperatures \[{{127}^{o}}C\] and \[{{527}^{o}}C\] respectively. The ratio of energy radiated by \[P\] and \[Q\] is                                           [MP PMT 1994]

    A)            0.054                                       

    B)            0.0034

    C)            1    

    D)            2

    Correct Answer: C

    Solution :

                       Total energy radiated from a body \[Q=A\varepsilon \sigma {{T}^{4}}t\] Þ \[Q\propto A{{T}^{4}}\propto {{r}^{2}}{{T}^{4}}\]     (Q \[A=4\pi {{r}^{2}})\] Þ \[\frac{{{Q}_{P}}}{{{Q}_{Q}}}={{\left( \frac{{{r}_{P}}}{{{r}_{Q}}} \right)}^{2}}\,{{\left( \frac{{{T}_{P}}}{{{T}_{Q}}} \right)}^{4}}={{\left( \frac{8}{2} \right)}^{2}}\,{{\left\{ \frac{(273+127)}{(273+527)} \right\}}^{4}}=1\]


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